RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

 Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 183–194 (Mi timm435)

Minimax and viscosity solutions in optimization problems for hereditary systems

N. Yu. Lukoyanov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: For a dynamical system with discrete and distributed time delays, a control problem under disturbance or counteraction is considered. The problem is formalized in the context of the game-theoretical approach in the class of control strategies with memory. The problem is associated with a functional Hamilton–Jacobi type equation with coinvariant derivatives. The minimax and viscosity approaches to a generalized solution of this equation are discussed. It is shown that, under the same condition at the right endpoint, the minimax and viscosity solutions coincide, thereby uniquely defining the functional of optimal guaranteed result in the control problem

Keywords: optimal control, differential games, time-delay systems, Hamilton–Jacobi equations, minimax solution, viscosity solution.

Full text: PDF file (213 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S214–S225

Document Type: Article
UDC: 517.977

Citation: N. Yu. Lukoyanov, “Minimax and viscosity solutions in optimization problems for hereditary systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 183–194; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S214–S225

Citation in format AMSBIB
\Bibitem{Luk09} \by N.~Yu.~Lukoyanov \paper Minimax and viscosity solutions in optimization problems for hereditary systems \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2009 \vol 15 \issue 4 \pages 183--194 \mathnet{http://mi.mathnet.ru/timm435} \elib{http://elibrary.ru/item.asp?id=12952764} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2010 \vol 269 \issue , suppl. 1 \pages S214--S225 \crossref{https://doi.org/10.1134/S0081543810060179} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962468865} 

• http://mi.mathnet.ru/eng/timm435
• http://mi.mathnet.ru/eng/timm/v15/i4/p183

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. Yu. Lukoyanov, “On Hamilton–Jacobi formalism in time-delay control systems”, Tr. IMM UrO RAN, 16, no. 5, 2010, 269–277
2. Bayraktar E., Keller Ch., “Path-Dependent Hamilton–Jacobi Equations in Infinite Dimensions”, J. Funct. Anal., 275:8 (2018), 2096–2161
•  Number of views: This page: 279 Full text: 100 References: 31